A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil?

Self inductance L is proportional to μN²/l where N is the number of turns and l is the length.
When the linear dimension is increased by a factor of 3, the length l increases by a factor of 3.
The number of turns N is proportional to the length. Thus N increases by a factor of 3.
Then L is proportional to (3N)²/(3l) = 9N²/3l = 3N²/l.
Therefore, the self inductance increases by a factor of 3.